## Symbolic Representation

The problem can be converted into a symbolic representation as follows:

Let's denote:
- $x_1$ as the acres of corn
- $x_2$ as the acres of cabbage

The objective is to maximize profit, which can be represented as:
\[ \text{Maximize:} \quad 50x_1 + 70x_2 \]

Subject to the constraints:
1. Total land constraint: $x_1 + x_2 \leq 200$
2. Tractor time constraint: $1x_1 + 1.5x_2 \leq 200$
3. Hand-picking time constraint: $2x_1 + 3x_2 \leq 275$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'acres of corn'), ('x2', 'acres of cabbage')],
    'objective_function': '50*x1 + 70*x2',
    'constraints': [
        'x1 + x2 <= 200',
        'x1 + 1.5*x2 <= 200',
        '2*x1 + 3*x2 <= 275',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Farmer_Problem")

# Define variables
x1 = model.addVar(name="corn_acres", lb=0, ub=200, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="cabbage_acres", lb=0, ub=200, vtype=gp.GRB.CONTINUOUS)

# Objective function: Maximize profit
model.setObjective(50*x1 + 70*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 + x2 <= 200, name="land_constraint")
model.addConstr(x1 + 1.5*x2 <= 200, name="tractor_constraint")
model.addConstr(2*x1 + 3*x2 <= 275, name="hand_picking_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal acres of corn: {x1.varValue}")
    print(f"Optimal acres of cabbage: {x2.varValue}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("The model is infeasible.")
```